(a)

Perimeter of the rectungular feild is feet.

Area of the rectungular feild must be atleast sq feet.

Formula for perimeter of the rectangle is .

.

The area of a rectangle is .

Substitute  and  to write an inequality that could be used to find the possible lengths to which the field can be constructed.

The inequality that is used to find the possible lengths to which the feild is to be constructed is .

(b)

The inequality is .

Let .

The factored form of is .

Therefore has real zeros at and .

Create a sign chart using the values and .

Note : The solid circle denote that the value are included in the solution set.

Observe the sign chart :

The set of value of denoted in blue color represents the solution set.

Determine whether is positive or negative on the test intervals.

Test intervals are and .

If ,then .

If , then .

If ,then .

The solutions of are values such that is positive or equal to .

From the chart the solution set is .

Therefore the length of the playing feild is minimum of feet and maximum of feet.

(c)

If the area of the field is to be no more than square feet, the inequality becomes Notice that the area of the field must be greater than .

.

Consider .

Since the length,width and area of the rectangle must be positive

The solutions of or are  values such that is negative or equal to .

From the sign chart, the solution set is .

Since the solution set is .

The area of the playing field must be greater than sq ft but at most sq ft.

The solution is or .

(a).

.

(b).

The solution set is .

The length of the playing feild is minimum of feet and maximum of feet.

(c).

or .